Mean-field type quadratic BSDEs

IF 1.1 Q2 MATHEMATICS, APPLIED

Numerical Algebra Control and Optimization Pub Date : 2023-01-01 DOI:10.3934/naco.2022009

Hélène Hibon, Ying Hu, Shanjian Tang

引用次数: 3

Abstract

In this paper, we give several new results on solvability of a quadratic BSDE whose generator depends also on the mean of both variables. First, we consider such a BSDE using John-Nirenberg's inequality for BMO martingales to estimate its contribution to the evolution of the first unknown variable. Then we consider the BSDE having an additive expected value of a quadratic generator in addition to the usual quadratic one. In this case, we use a deterministic shift transformation to the first unknown variable, when the usual quadratic generator depends neither on the first variable nor its mean. The general case can be treated by a fixed point argument.

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平均场型二次BSDEs

本文给出了二次型BSDE的可解性的几个新结果，该方程的生成器也依赖于两个变量的均值。首先，我们使用BMO鞅的John-Nirenberg不等式来考虑这样的BSDE，以估计其对第一个未知变量的演化的贡献。然后，我们考虑BSDE除了通常的二次生成器之外，还具有二次生成器的附加期望值。在这种情况下，当通常的二次生成器既不依赖于第一个变量也不依赖于它的平均值时，我们对第一个未知变量使用确定性移位变换。一般情况可以用不动点论证来处理。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Numerical Algebra Control and Optimization MATHEMATICS, APPLIED-

CiteScore

3.10

自引率

0.00%

发文量

期刊介绍： Numerical Algebra, Control and Optimization (NACO) aims at publishing original papers on any non-trivial interplay between control and optimization, and numerical techniques for their underlying linear and nonlinear algebraic systems. Topics of interest to NACO include the following: original research in theory, algorithms and applications of optimization; numerical methods for linear and nonlinear algebraic systems arising in modelling, control and optimisation; and original theoretical and applied research and development in the control of systems including all facets of control theory and its applications. In the application areas, special interests are on artificial intelligence and data sciences. The journal also welcomes expository submissions on subjects of current relevance to readers of the journal. The publication of papers in NACO is free of charge.